Nuprl Lemma : pseudo-positive-is-positive-proof2
∀x:ℝ. r0 < x supposing pseudo-positive(x)
Proof
Definitions occuring in Statement :
pseudo-positive: pseudo-positive(x),
rless: x < y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
sq_type: SQType(T),
guard: {T},
false: False,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
int_upper: {i...},
rneq: x ≠ y,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
isl: isl(x),
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat-star: ℕ*,
int_seg: {i..j-},
lelt: i ≤ j < k,
so_apply: x[s],
top: Top,
cauchy: cauchy(n.x[n]),
sq_exists: ∃x:A [B[x]],
assert: ↑b,
bnot: ¬bb,
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
absval: |i|,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
cand: A c∧ B,
nat-star-retract: nat-star-retract(s),
rless: x < y,
rge: x ≥ y,
sq_stable: SqStable(P),
real: ℝ,
converges: x[n]↓ as n→∞,
pseudo-positive: pseudo-positive(x),
stable: Stable{P},
label: ...$L... t,
l_all: (∀x∈L.P[x]),
isr: isr(x)
Latex:
\mforall{}x:\mBbbR{}. r0 < x supposing pseudo-positive(x)
Date html generated:
2020_05_20-AM-11_19_27
Last ObjectModification:
2020_01_03-PM-04_19_12
Theory : reals
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